Djokovic, ranked No. 3 in the world, drew the best-of-five series' first match against Russia's Mikhail Youzhny, ranked eighth in the world. The other singles match Friday sends Serbia's Viktor Troicki -- 114th in the world -- against fourth-ranked Nikolay Davydenko.
The reverse singles Sunday have Davydenko playing Djokovic and Youzhny meeting Troicki.
The matches are to be played on a hard court at the Luzhniki Olympic Complex in Moscow.
Russia finished second to the United States for the 2007 Davis Cup title after winning the title in 2002 and 2006. The Russians are 2-1 against Serbia in Davis Cup play.
The Serbia-Russia winner advances to an April series against the winner of the Belgium-Czech Republic match.